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Polytope of Type {4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2}*768d
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 16, 96, 48, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12,2}*384b, {4,6,2}*384b, {4,12,2}*384c
   4-fold quotients : {4,12,2}*192a, {4,12,2}*192b, {4,12,2}*192c, {4,6,2}*192
   8-fold quotients : {2,12,2}*96, {4,6,2}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   12-fold quotients : {4,4,2}*64
   16-fold quotients : {4,3,2}*48, {2,6,2}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {2,3,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)
(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)
(42,44)(45,47)(46,48)(49,63)(50,64)(51,61)(52,62)(53,67)(54,68)(55,65)(56,66)
(57,71)(58,72)(59,69)(60,70)(73,87)(74,88)(75,85)(76,86)(77,91)(78,92)(79,89)
(80,90)(81,95)(82,96)(83,93)(84,94);;
s1 := ( 1,49)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)(10,55)
(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)(21,65)
(22,67)(23,66)(24,68)(25,73)(26,75)(27,74)(28,76)(29,81)(30,83)(31,82)(32,84)
(33,77)(34,79)(35,78)(36,80)(37,85)(38,87)(39,86)(40,88)(41,93)(42,95)(43,94)
(44,96)(45,89)(46,91)(47,90)(48,92);;
s2 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)(18,20)
(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)(49,81)
(50,84)(51,83)(52,82)(53,77)(54,80)(55,79)(56,78)(57,73)(58,76)(59,75)(60,74)
(61,93)(62,96)(63,95)(64,94)(65,89)(66,92)(67,91)(68,90)(69,85)(70,88)(71,87)
(72,86);;
s3 := (97,98);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)
(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)
(41,43)(42,44)(45,47)(46,48)(49,63)(50,64)(51,61)(52,62)(53,67)(54,68)(55,65)
(56,66)(57,71)(58,72)(59,69)(60,70)(73,87)(74,88)(75,85)(76,86)(77,91)(78,92)
(79,89)(80,90)(81,95)(82,96)(83,93)(84,94);
s1 := Sym(98)!( 1,49)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)
(10,55)(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)
(21,65)(22,67)(23,66)(24,68)(25,73)(26,75)(27,74)(28,76)(29,81)(30,83)(31,82)
(32,84)(33,77)(34,79)(35,78)(36,80)(37,85)(38,87)(39,86)(40,88)(41,93)(42,95)
(43,94)(44,96)(45,89)(46,91)(47,90)(48,92);
s2 := Sym(98)!( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)
(18,20)(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)
(49,81)(50,84)(51,83)(52,82)(53,77)(54,80)(55,79)(56,78)(57,73)(58,76)(59,75)
(60,74)(61,93)(62,96)(63,95)(64,94)(65,89)(66,92)(67,91)(68,90)(69,85)(70,88)
(71,87)(72,86);
s3 := Sym(98)!(97,98);
poly := sub<Sym(98)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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